Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1044 |
| commutator, hypocenter | C52 | C2×C16 |
| Frattini | C4 | C2×#1044 |
| Fitting | C52×C8 | C4 |
| socle | C2×C52 | C2×C8 |
| prime radical | C2×C5⋊D5 | C8 |
| cosocle | #6029 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=d,d^2=e,f^a=f^3,g^a=g^2,f^c=f^4,g^c=g^480 conjugacy classes — view the full character table.
| maximal subgroup of | #13099848, #13099850, #13099854, … |
| maximal normal subgroup of | #13099848, #13099850, #13099854, … |
| maximal quotient of | #13100313, #13100314, #13100355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 541);